Nonlocal Boundary Value Problems for Hilfer Generalized Proportional Fractional Differential Equations
Open Access
- 13 March 2022
- journal article
- research article
- Published by MDPI AG in Fractal and Fractional
- Vol. 6 (3) , 154
Abstract
In this paper, we discuss the existence and uniqueness of solutions for boundary value problems for Hilfer generalized proportional fractional differential equations with multi-point boundary conditions. Firstly, we consider the scalar case for which the uniqueness result is proved by using Banach’s fixed point theorem and the existence results are established via Krasnosel’skiĭ’s fixed point theorem and Leray–Schauder nonlinear alternative. We then establish an existence result in the Banach space case based on Mönch’s fixed point theorem and the technique of the measure of noncompactness. Examples are constructed to illustrate the application of the main results. We emphasize that, in this paper, we initiate the study of Hilfer generalized proportional fractional boundary value problems of order in (1, 2].Keywords
This publication has 30 references indexed in Scilit:
- New direction in fractional differentiation2017
- On the generalized fractional derivatives and their Caputo modificationJournal of Nonlinear Sciences and Applications, 2017
- A Caputo fractional derivative of a function with respect to another functionCommunications in Nonlinear Science and Numerical Simulation, 2017
- On conformable fractional calculusJournal of Computational and Applied Mathematics, 2015
- A new definition of fractional derivativeJournal of Computational and Applied Mathematics, 2014
- A Note on Fractional Order Derivatives and Table of Fractional Derivatives of Some Special FunctionsAbstract and Applied Analysis, 2013
- Caputo-type modification of the Hadamard fractional derivativesAdvances in Difference Equations, 2012
- New approach to a generalized fractional integralApplied Mathematics and Computation, 2011
- Recent applications of fractional calculus to science and engineeringInternational Journal of Mathematics and Mathematical Sciences, 2003
- Boundary value problems for nonlinear ordinary differential equations of second order in Banach spacesNonlinear Analysis, 1980